Causality Without Causal Models
Joseph Y. Halpern, Rafael Pass
TL;DR
This work generalizes Halpern-Pearl's actual causality beyond causal models to a broad class of counterfactual frameworks (ccfs). It defines an abstract causality notion parameterized by a language ${\cal L}$ and witness formulas, showing that the HP definition is recovered when ${\cal L}$ restricts to conjunctions of primitive events and that backtracking can be handled by appropriate language choices. The authors connect causal models and Lewis-style counterfactual structures as instances of ccfs and prove key correspondences (e.g., equivalence under strong consistency with recursive models). They further extend the framework to an abstract notion of explanation, tying it to agent knowledge via epistemic contexts. Overall, the paper provides a versatile, language-sensitive foundation for causality and explanation that accommodates richer counterfactuals, beliefs, and backtracking across diverse reasoning formalisms.
Abstract
Perhaps the most prominent current definition of (actual) causality is due to Halpern and Pearl. It is defined using causal models (also known as structural equations models). We abstract the definition, extracting its key features, so that it can be applied to any other model where counterfactuals are defined. By abstracting the definition, we gain a number of benefits. Not only can we apply the definition in a wider range of models, including ones that allow, for example, backtracking, but we can apply the definition to determine if A is a cause of B even if A and B are formulas involving disjunctions, negations, beliefs, and nested counterfactuals (none of which can be handled by the Halpern-Pearl definition). Moreover, we can extend the ideas to getting an abstract definition of explanation that can be applied beyond causal models. Finally, we gain a deeper understanding of features of the definition even in causal models.